How do you calculate the line current in a delta connection?

In a three-phase delta connection, the load is connected in a triangular or delta configuration. Each phase has a load impedance (usually expressed in terms of resistance and reactance).

Let's assume we have three phase currents labeled as Ia, Ib, and Ic. The line currents can be calculated using the following formula:

For balanced loads:

In a balanced delta connection, the phase currents (Ia, Ib, and Ic) are equal in magnitude and are separated by 120 degrees in a three-phase system. In this case, the line current (IL) can be calculated as:

IL = Ia

For unbalanced loads:

In an unbalanced delta connection, the phase currents are not equal or not 120 degrees apart. In this case, you can calculate the line current (IL) using vector addition of the phase currents:

IL = |Ia + Ib + Ic|

Here, "|" denotes the magnitude of the vector sum of the phase currents.

Keep in mind that when dealing with unbalanced loads, the phase currents might be represented as complex numbers (consisting of both magnitude and phase angle) or as vectors in a two-dimensional plane. In such cases, you may need to use vector addition techniques, taking both magnitude and phase angle into account.

Also, remember that the line currents in a delta connection are generally higher than the corresponding phase currents due to the delta configuration's nature. So, it's essential to consider this when sizing protective devices and conducting load calculations.